Mathematical modeling and forming method of rake face of toroidal worm gear hob based on conical production surface

Abstract

In order to improve the cutting performance of toroidal worm gear hob and the tooth surface accuracy of hobbing worm gear, to control the absolute value of the side rake angle of each cutter tooth to be smaller and more balanced on the left and right sides, a method of developing the rake face of toroidal worm gear hob with spiral groove by using conical production surface is proposed. According to the theory of gear meshing rationality, the mathematical model of the rake face is established. The analysis and calculation example results show that the absolute value of the rake angle on both sides changes with the transmission ratio coefficient. By studying this change law, the optimal milling transmission ratio coefficient k = 0.886 is obtained. Meanwhile, the corresponding absolute value of the rake angle is between ±4.5°, which reduce the absolute value of the rake angles on both sides of the cutter teeth effectively and make the rake angles on the left and right sides be more balanced. The spiral groove was simulated, and the rake angle was measured in the simulation software. The measured results are consistent with the calculated results, which prove the correctness of this method.